Check column 600x400 with 8-28 mm bars

Data

• Column 400 × 600 mm, 8-28 mm bars ($A_{sc} = 4926$ mm², $p = 2.05\%$), arranged 3 bars on each 400 mm face and 1 bar at mid-height of each side (3-2-3 arrangement). Effective cover $d' = 60$ mm, so $d'/D = 0.10$ (major axis) and $d'/b = 0.15$ (minor axis).
• $P_u = 2000$ kN, $M_{ux} = 350$ kN·m (about the major axis), $M_{uy} = 50$ kN·m; M20 concrete, Fe415 steel. The column is taken as short (no length is given), and the moments are larger than $P_u e_{min}$ (about 40 kN·m), so they are used as given.

Uniaxial capacities at $P_u$ = 2000 kN

$\dfrac{P_u}{f_{ck} bD} = \dfrac{2000000}{20 \times 400 \times 600} = 0.417$ and $\dfrac{p}{f_{ck}} = 0.103$. From the SP-16 interaction chart for Fe415 (or equivalently by strain compatibility, computed here):

• About the major axis: $M_{ux1} = 356.1$ kN·m
• About the minor axis: $M_{uy1} = 213.9$ kN·m

Biaxial check (IS 456 cl. 39.6)

$P_{uz} = 0.45 f_{ck} A_c + 0.75 f_y A_{sc} = 0.45 \times 20 \times 235074 + 0.75 \times 415 \times 4926 = 3649$ kN $\dfrac{P_u}{P_{uz}} = 0.548$, so $\alpha_n = 1.58$ (linear interpolation between 1.0 at 0.2 and 2.0 at 0.8).

$$\left(\frac{M_{ux}}{M_{ux1}}\right)^{\alpha_n} + \left(\frac{M_{uy}}{M_{uy1}}\right)^{\alpha_n} = \left(\frac{350}{356.1}\right)^{1.58} + \left(\frac{50}{213.9}\right)^{1.58} = 1.074$$

Since 1.074 $> 1.0$, the column is not safe for the given combination of load and moments; the section or the steel must be increased.